WARM UP Find the product. 1.) (m – 8)(m – 9) 2.) (z + 6)(z – 10) 3.) (y + 20)(y – 20)

Algebra II 4.3 SOLVE X 2 + BX + C = 0 BY FACTORING

OBJECTIVE Solve quadratic equations.

VOCABULARY Monomial – an expression that is either a number, a variable, or the product of a number and one or more variables. Binomial – sum of two monomials. Trinomial – sum of three monomials.

EXAMPLE 1 – FACTOR TRINOMIALS IN THE FORM AX 2 + BX + C = 0 Factor the expression. A.) x x + 48 B.) x 2 – 9x - 5

SPECIAL FACTORING PATTERNS Difference of two squares pattern a 2 – b 2 = (a + b)(a – b) Example: x 2 – 4 = (x +2)(x – 2)

SPECIAL FACTORING PATTERNS CONTINUED Perfect Square Trinomial a 2 + 2ab + b 2 = (a + b) 2 Example: x 2 + 6x + 9 = (x +3) 2 a 2 – 2ab + b 2 = (a – b) 2 Example: x 2 – 4x + 4 = (x – 2) 2

EXAMPLE 2 – FACTOR WITH SPECIAL PATTERNS Factor the expression. A.) m 2 – 121 B.) r r + 49 C.) p 2 – 24p + 144

WARM UP Find the product. A.) (d + 9) 2 B.) (x – 14) 2 Factor the expression. C.) x 2 – 9x + 20

ZERO PRODUCT PROPERTY If the product of two expressions is zero, then one or both of the expressions equal zero. Example: If (x + 5)(x + 2) = 0, then x + 5 = 0 or x + 2 = 0. That is, x = -5 or x = -2.

EXAMPLE 3 What are the roots of the equation x 2 – x – 42 = 0?

EXAMPLE 5 – FIND THE ZEROS OF THE QUADRATIC FUNCTIONS Find the zeros of the function by rewriting the function in intercept form. y = x 2 + 3x - 28

ASSIGNMENT Pg. 255 – 256 (10 – 32 even)